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**what does it mean for a set to be bounded??**

in the context of the hein-borel theorem

i mean the mathematically rigorous definition

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- Thread starter royzizzle
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- #1

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in the context of the hein-borel theorem

i mean the mathematically rigorous definition

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Office_Shredder

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S a subset of R

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Another equivalent definition is that it has finite diameter, where

[tex]\mathrm{diam}(S) = \sup_{x, y \in S}(\mathrm{dist}(x, y)).[/tex]

This is applicable to any metric space (though the Heine-Borel theorem is not!).

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